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We always start by noting the values that would cause any denominators to be zero.
Solve:
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Note any value of the variable that would make any denominator zero. |
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Find the least common denominator of all denominators in the equation. The LCD is . | |
Clear the fractions by multiplying both sides of the equation by the LCD. |
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Distribute. |
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Multiply. |
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Solve the resulting equation. First write the quadratic equation in standard form. |
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Factor. |
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Use the Zero Product Property. |
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Solve. |
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Check. | |
We did not get 0 as an algebraic solution. | |
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Solve:
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Note any value of the variable that would make any denominator zero. |
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Find the least common denominator of all denominators in the equation. The LCD is . | |
Clear the fractions by multiplying both sides of the equation by the LCD. |
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Remove common factors. |
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Simplify. |
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Multiply. |
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Solve the resulting equation. |
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We did not get 0 or as algebraic solutions. | |
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When one of the denominators is a quadratic, remember to factor it first to find the LCD.
Solve:
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Note any value of the variable that would make any denominator zero. |
![]() |
Find the least common denominator of all denominators in the equation. The LCD is . | |
Clear the fractions by multiplying both sides of the equation by the LCD. |
![]() |
Distribute. |
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Remove common factors. |
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Simplify. |
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Distribute. |
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Solve. |
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We did not get as algebraic solutions. | |
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Solve:
![]() | |
Note any value of the variable that would make any denominator zero. |
![]() |
Find the least common denominator of all denominators in the equation. The LCD is . | |
Clear the fractions by multiplying both sides of the equation by the LCD. |
![]() |
Distribute. |
![]() |
Remove common factors. |
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Simplify. |
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Simplify. |
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Combine like terms. |
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Solve. First write in standard form. |
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Factor. |
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Use the Zero Product Property. |
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We did not get 4 or 3 as algebraic solutions. | |
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Solve:
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Factor all the denominators, so we can note any value of the variable the would make any denominator zero. |
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Find the least common denominator of all denominators in the equation. The LCD is . | |
Clear the fractions. |
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Distribute. |
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Remove common factors. |
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Simplify. |
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Solve the resulting equation. |
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Check. The only algebraic solution was 4, but we said that 4 would make a denominator equal to zero. The algebraic solution is an extraneous solution. There is no solution to this equation. |
The equation we solved in [link] had only one algebraic solution, but it was an extraneous solution. That left us with no solution to the equation. Some equations have no solution.
Solve:
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Note any value of the variable that would make any denominator zero. |
![]() |
Find the least common denominator of all denominators in the equation. The LCD is . | |
Clear the fractions by multiplying both sides of the equation by the LCD. |
![]() |
Distribute. |
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Remove common factors. |
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Simplify. |
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Solve the resulting equation. |
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Check. | |
is an extraneous solution. | |
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